Computing discrete shape operators on general meshes

Eitan Grinspun, Yotam Gingold, Jason Reisman, Denis Zorin

Research output: Contribution to journalArticlepeer-review


Discrete curvature and shape operators, which capture complete information about directional curvatures at a point, are essential in a variety of applications: simulation of deformable two-dimensional objects, variational modeling and geometric data processing. In many of these applications, objects are represented by meshes. Currently, a spectrum of approaches for formulating curvature operators for meshes exists, ranging from highly accurate but computationally expensive methods used in engineering applications to efficient but less accurate techniques popular in simulation for computer graphics. We propose a simple and efficient formulation for the shape operator for variational problems on general meshes, using degrees of freedom associated with normals. On the one hand, it is similar in its simplicity to some of the discrete curvature operators commonly used in graphics; on the other hand, it passes a number of important convergence tests and produces consistent results for different types of meshes and mesh refinement.

Original languageEnglish (US)
Pages (from-to)547-556
Number of pages10
JournalComputer Graphics Forum
Issue number3
StatePublished - Sep 2006

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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